Command of a non-linear model in discrete-time of the recidivism phenomenon in Morocco

Abstract

The phenomenon of recidivism is considered to be one of the significant characteristics of the performance of the penitentiary and reintegration system, as well as the effectiveness of the judicial and penal system of such a society. In this paper, we define a mathematical model of a dynamic system of non-linear differential equations in discrete time which describes the observation conceptually and exposes this phenomenon by taking into account four types of variables named; Susceptible Prisoners, Infected Prisoners (Recidivists), Exposed Prisoners and Recovred Prisoners. Our ambition behind this study is to characterise an optimal control that minimises the number of recidivist prisoners after their release, by defining two strategic controls which are respectively, an awareness programme through education in detention centres and socio-economic support with follow-up after release, with the aim of guiding public policy makers in their implementation to determine effective conditions aimed at combating this scourge. The characterisation of the optimal control analysis sought is based on the principle of Pontryagin’s maximum, the objective of which is to minimise the numbers of recidivist individuals and inmates potentially susceptible to recidivate, in order to maximise the number of post-releases. The numerical simulation was performed using Python 3.12.3. Consequently, numerical illustrations of the results obtained are given, confirming the performance of the optimisation strategy followed.